FM's Archaeo-Astronomy Topic - the basics

[Forum Monk]

Welcome to FM's Basics of Archaeo-astronomy

I will try to present the concepts of archaeo-astronomy in an easy to understand way using simple graphics and animated models. Your comments are welcome. If anything is unclear or requires further explanation as we go along, please feel free to let me know.

I will be making several posts over a period of days or weeks. Since I have no particular plan in mind, the series may be a bit disjointed or may not flow well but I hope to cover relevent backgrounds for future archae--astronomy topics.

[Forum Monk]

Here is the earth -



The earth is tilted on its axis of rotation from true vertical about 23.5 degrees. This angle is called the angle of obliquity. In reality this angle changes +/- 1 degree over a period of 41,000 years but for the purposes of this series we will ignore this fact and consider the obliquity to be a fixed, unchanging angle.

The earth spins on its axis one complete revolution every 24 hours. We define an hour as one 24th of 360 degrees. So each hour the earth has spun 15 degrees on its axis and in one day, 360 degrees. So if we mark the length of a day as the time from one sun at zenith until the next sun at zenith we have defined a solar day. Modern clocks will find that the length of the day will vary by a slight amount positive or negative so the solar day is on average exactly 24 hours. Ancient people can easily measure time by a simple sundial or gnomon. Sometime before 2000BCE water clocks were developed to keep track of time.

We could also define the length of a day as the amount of time from a certain star at zenith until the next time the same star reaches zenith. However, if the two periods are compared, one would discover that the stellar day is about 4 minutes shorter than the solar day. This is because the earth is orbiting the sun all the while it is spinning on its axis.

If one could look past the sun at zenith and see a distant star, it would be possible to directly observe the earth's orbit around the sun.


In the above picture we see a star and the sun at zenith. We will look for the same star to reach zenith the next day. meanwhile the earth is traveling around the sun on its annual orbit.

The next day the star reaches zenith -


But because the earth's position has changed relative to the sun (which is much closer than a distant star), it will take another four minutes before we see the sun at zenith, but then the star will no longer appear at zenith. The sun and the star will not be aligned again until the earth has completely circled the sun and returns to the same position it was in in the first picture one year in the future.

[Forum Monk]

The earth revolves (orbits) around the sun. The orbit is actually elliptical in shape but the ellipse is very close to circular with a eccentricity of 0.017 (0.000 would be a perfect circle). It takes an average of 365.25 days for the earth to make one complete orbit around the sun.



The obliquity of the earth in relation to the orbit around the sun is responsible for the variation in seasons. In the picture are four views of the earth as it revolves around the sun. On the right side of the picture, the earth's southern hemisphere is tilted toward the earth and the northern hemisphere away. It would be summer in the south and winter in the north.

Three months later the earth would be 1/4 of the way around the sun (see the top of the picture). The northern and southern hemispheres are at the same angle from the sun (though the earth's axis remains ever tilted) and so the south is experiencing autumn while the north experiences spring.

In another three months, the northern hemisphere is tilted toward the sun and southern away as the north now enjoys summer while the south experiences winter.

Three months more (nine months from the start) the two hemispheres again are equal as the north moves toward autumn and south toward spring.

Now this may seem elementary to you but some important observations should be made. Because the earth is orbiting the sun, its position in space is changing and as we have seen in the previous post, the more distant stars appear to be rising four minutes earlier each day relative to the sun. The fixed star we see in the previous post will be reaching zenith a full twelve hours ahead of the sun in six months time and will again realign in 12 months time. During the course of a year, all of the constellation visible from a given location will parade overhead, ever shifting ahead by four minutes per day.

It is easy to understand therefore, how certain groups of stars are associated with certain seasons of the year, since they are only seen at culmination (zenith) during those seasons. For example, the eqyptians learned that the appearance of the star Sirius, preceeded a season of flooding of the Nile River.

[Forum Monk]

Without doubt, the ancient peoples must have realized that the sun, moon and planets appeared to move differently than the stars and at some point they undoubtedly figured out that the sun and moon and probably the planets were not as far away as the stars because they appear larger and brighter and would at times obscure the stars behind them.

Is it possible, they realized the stellar (sidereal) day was shorter than the solar day? I doubt it. Our illustration demonstrates observation of a star and the sun at the same time but this is not possible. Obviously solar observation and measurment only occurs in daylight and stellar observation after the sky has sufficiently darkened. So the question is...if you were an ancient astronomer, would you synchronize time to the sun or the stars?

I guess it depends on the culture and we now know different cultures or disciplines used different methods.

[Forum Monk]

The earth also has another type of motion caused by the gravity of the sun and moon tugging on the earth. The earth is not a perfect sphere. Its diameter through the equator is larger than its diameter through the poles so it is essentially flattened a bit on the top and bottom, defining the shape of an oblate spheroid. Lunisolar gravity generates a torque as it pulls on the bulging equator causing a wobble of the polar axis as it spins. In effect, the polar axis scribes a circular path taking approximately 25,800 years to complete one revolution.



This motion has no effect on the tilt of the earth. It remains "fixed", but as can be seen in the animation, the pole will point toward different locations with respect to the northern stars as it sweeps out its circular path. Today the pole is pointing toward the star Polaris in the constellation Ursa Minor (the "Little Dipper"), 3000 years ago it was pointing toward the star Thuban in the constellation Draco. In 12,000 years it will be pointing toward the bright Vega in the constellation Lyra. A similar sweeping through the southern pole stars is apparent in the southern hemisphere.


The picture above shows the circle swept out by the northern polar axis through various epochs of time. In the year 2000 we were in epoch +2000, a position very close to the star Polaris in the end of the handle of Ursa Major (the Little Dipper).

[Forum Monk]

Enough for now - feel free to post any comments or ask questions about the above posts.

[MichelleH]

Monk,

This is great work and thank you! Please continue and let me know if you want this moved to the discussion section instead of the 'off' topic forum.

There is great relevance in this field of study.


Michelle

[War Arrow]

Fascinating stuff, FM, and nicely explained. One question occurs:

Lunisolar gravity generates a torque as it pulls on the bulging equator causing a wobble of the polar axis as it spins. In effect, the polar axis scribes a circular path taking approximately 25,800 years to complete one revolution.

I'm looking at your graphic here and getting the impression that this might mean the seasons shift over large spans of time. Does this mean that a present day summer would have been a winter 12,900 years ago (ie with the Earth at one specific position in relation to the sun, but with the tilt of its axis in the oposite direction to its present position). Not sure if that question even makes sense so apologies if I've missed something there.
Once again, impressive bit of work.

[kbs2244]

Oh yeah!
Keep it coming.
This can be such a help in dating.

[Forum Monk]

I'm looking at your graphic here and getting the impression that this might mean the seasons shift over large spans of time. Does this mean that a present day summer would have been a winter 12,900 years ago (ie with the Earth at one specific position in relation to the sun, but with the tilt of its axis in the oposite direction to its present position). Not sure if that question even makes sense so apologies if I've missed something there.

Your question brings a brilliant smile to my face War Arrow, because your observation is spot on. In fact it is the point I was going to built to and perfectly demonstrates how precession will eventually show itself by the shifting of the seasons. It is a fact many have failed to realized today when they speak of a moving equinox. Obviously if the equinox moves then the spring is moving as well and so the seasonal association with stars by necessity has changed significantly over the last 6000 years of known history.

Very good WA. You have earned an "A+".

[War Arrow]

Bloody hell!

I was almost wincing when I typed out that post, thinking "well... he's gonna think I'm an idiot, but I'd better ask just in case."

I've just tried to work out how many years it would take for the equinox to drift by a day, but the figure seems a bit improbable to me so I think I've got my sums wrong.
I think I'd better shut up and let you handle this one.

[Forum Monk]

The answer should come as no surprise. It is oft quoted the eqinox drifts 1 degree in 72 years (25800 years / 360 degrees)=71.6 years per degree. So, since the equinox will move through 365.25 days (one year) in one precessional cycle, the date will shift one day every 70.6 years (=25800 / 365.25).

[War Arrow]

For some reason I got a 1 day shift every 16 years which seemed a bit ridiculous. Surprised that it's 70 though. That's quite a significant drift.

[Forum Monk]

The path the sun appears to follow across the sky, is called the ecliptic and it lies on the ecliptical plane. In fact the orbit of all the planets lies more or less, on the ecliptical plane.



If we define the plane of the ecliptic as being horizontal, then the earth is tilted 23.5 degrees with respect to the horizontal. The celestial equator and celestial poles are tilted off horizontal due to the axial tilt of the earth.



From the earth perspective, the ecliptic is tilted since it is natural to visualize the celestial north pole as being directly over the earth's axial pole and south celestial pole as an extension of the earth's south axial pole. This puts the earth's equator and the celestial equator on the same plane.

[Forum Monk]

So, standing on the equator, looking at the path of the sun (the ecliptic), the path seems to change over the course of the year because of the axial tilt of the earth. During the summer (northern summer) the sun will appear as much as 23.5 degrees north of the equator and in winter, 23.5 degree south of the equator.



The only time the sun would be directly overhead is during the spring or autumn equinox.

But as has been already observed, by one reader of this thread, the lunisolar wobble of the earth also affects the apparent location of the ecliptic in exactly the same way as its annual orbit around the sun.

During half the cycle, the earth is tilted toward the sun and during half it is tilted away and so, depending on where the wobble cycle is, summer, winter and equinoxes are all shifted accordingly. And since the wobble is moving opposite of the other earth movements, the seasons appear to shift back in time. In other words they precess; hence the term precession of the equinox.

Precession may also be called lunisolar precession or when considering the combined effect of all solar system objects on the wobble of the earth; general precession.